Question

Find the measure of an angle if 7 times its complement is 10 degree less than three times its supplement

Answer 1

Answer:

25

Step-by-step explanation:

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Answer 2

Answer:

the measure of the angle is 25°

Step-by-step explanation:

let  the angle be x

two angles are said to be complementary if their sum is 90

so x + complement of x = 90

so complement of x  = 90 - x        

7 times the complement of x = 7 (90 - x )    ..equation 1

two angles are said to be supplementary if their sum is 180

so x + supplement of x = 180

so supplement of x  = 180 - x

3 times the supplement of x = 3 ( 180 - x )   .. equation 2

but 7 times complement of x is 10 degree less than three times supplement of x

so from equations 1 and 2

7 (90 - x ) = 3 ( 180 - x ) - 10

=> 630 - 7x = 540 - 3x - 10

=> 630 - 540 + 10 = - 3x + 7x

=> 100 = 4x

=> x = 25

so the measure of the angle is 25°